How to control different parent
It looks like you parent the door object to the Empty Sphere, am I right? Don't do it, don't parent the door to the Empty Sphere, otherwise it won't be parented to the Empty Plain Axe anymore. Only parent the door to the Empty Plain Axe and the Empty Plain Axe (and the front of the object) to the Empty Sphere. When the Empty Sphere moves, the door will follow as it is child of its child. Is it not your problem?

To make it simple, let say you deparent everything to start from scratch, now what you need to do is : 1) parent the door to the Empty Plain Axe 2) parent the front and the Empty Plain Axe to the Empty Sphere.